Section 5.3
Problem Solving and Unit Conversions
Objectives
1. To learn how dimensional analysis can be used to solve
problems
2. To learn the three temperature scales
3. To learn to convert from one temperature scale to
another
4. To practice using problem solving techniques
5. To define density and its units
Section 5.3
Problem Solving and Unit Conversions
A. Tools for Problem Solving
• I am driving in Canada. I have a journey of 120 km and I
need to estimate how many liters of gas to buy. I know
my car fuel mileage is 24 miles per gallon. (1 mile is 1.6
km, 1 gallon is 3.79 liters)
• Be systematic
• Ask yourself these questions
– What do we know to start with?
– Where do we want to go?
– How do we get there?
– Does it make sense?
Section 5.3
Problem Solving and Unit Conversions
A. Tools for Problem Solving
Converting Units of Measurement
• We can convert from one system of units to another by a
method called dimensional analysis using conversion
factors.
• Unit1  conversion factor = Unit2
Section 5.3
Problem Solving and Unit Conversions
A. Tools for Problem Solving
Converting Units of Measurement
• Conversion factors are built from an equivalence
statement which shows the relationship between the
units in different systems.
1 inch = 2.54cm or 1 cm = 0.394 inches
• Conversion factors are ratios of the two parts of the
equivalence statement that relate the two units.
1 inch or 2.54cm or 0.394 inches or 1 cm .
2.54cm
1 inch
1 cm
0.394 inches
Section 5.3
Problem Solving and Unit Conversions
A. Tools for Problem Solving
Converting Units of Measure
2.85 cm = ? in.
2.85 cm  conversion factor = ? in.
Equivalence statement
2.54 cm = 1 in.
Possible conversion factors
Does this answer make sense?
Section 5.3
Problem Solving and Unit Conversions
A. Tools for Problem Solving
Tools for Converting from One Unit to Another
Step 1 Find an equivalence statement that relates the 2
units.
Step 2 Choose the conversion factor by looking at the
direction of the required change (cancel the
unwanted units).
Step 3 Multiply the original quantity by the conversion
factor.
Step 4 Make sure you have the correct number of
significant figures.
Go back and solve the Driving Problem in Canada
Section 5.3
Problem Solving and Unit Conversions
32 Degrees?
Section 5.3
Problem Solving and Unit Conversions
..or 32
Degrees?
Section 5.3
Problem Solving and Unit Conversions
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32 Degrees?
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Section 5.3
Problem Solving and Unit Conversions
B. Temperature Conversions
• There are three commonly used temperature scales,
Fahrenheit, Celsius and Kelvin.
Section 5.3
Problem Solving and Unit Conversions
B. Temperature Conversions
Converting Between the Kelvin and Celsius Scales
• Note that
– The temperature unit is the same size.
– The zero points are different.
• To convert from Celsius to Kelvin we need to adjust for
the difference in zero points.
Section 5.3
Problem Solving and Unit Conversions
B. Temperature Conversions
Converting Between the Kelvin and Celsius Scales
70 oC = ? K
TC + 273 = TK
70 + 273 = 343 K
Section 5.3
Problem Solving and Unit Conversions
B. Temperature Conversions
Converting Between the Fahrenheit and Celsius Scales
• Note
– The different size units
– The different zero points
• To convert between Fahrenheit and Celsius we need to
make 2 adjustments.
ToC = ?
Section 5.3
Problem Solving and Unit Conversions
Convert These Temperatures
200oC to K
-52oC to K
345K to oC
11K to oC
212oF to oC
32oF to oC
525oF to oC
25oC to oF
-20oC to oF
200oF to K
Section 5.3
Problem Solving and Unit Conversions
At what temperature would a Celsius and a
Fahrenheit thermometer read the same?
ToF
=
ToC
Section 5.3
Problem Solving and Unit Conversions
C. Density
• Density is the amount of matter present in a given
volume of substance.
Write down all the statements relating the three properties
D, M and V
Section 5.3
Problem Solving and Unit Conversions
How to Remember the Density Relationships
Q. Where do
you get your
permit?
A. At the DMV
m
D
v
Section 5.3
Problem Solving and Unit Conversions
Calculate the Missing Quantity:
Mass
Volume
4530 g
225 cm3
?
g/cm3
26.3g
25.0 mL
?
g/cm3
1.00 lb
500. cm3
?
g/cm3
0.352 g
0.000271 L
?
g/cm3
? g
45 cm3
2.45 g/cm3
1000 g
? mL
10.5 g/cm3
? g
10 L
0.0023 g/mL
1.45 kg
?L
2.67 g/mL
Remember the “DMV”
Density
1 lb = 454 g
Section 5.3
Problem Solving and Unit Conversions
C. Density
H2 = 0.084 kg/m3 Is the hydrogen number correct?
Section 5.3
Problem Solving and Unit Conversions
Density of Water
One gram of water has a volume of 1 milliliter
The density of water is……?
D = M/V
Density of water = 1 g/mL or 1g/cm3
How much does 150 mL of water weigh?
What is the density of water in kg/m3?
(Egg density demo)